Increasing concerns regarding wireless systems' security are leading researchers to exploit the physical properties of a medium while designing any secured wireless network. The secrecy performance of a mixed radio frequency-free space optical (RF-FSO) system with a variable gain relaying scheme is investigated in this paper under the attempt of wiretapping by an eavesdropper. We assume that the eavesdropper can intrude the target data from the RF link only. Both the RF links (main and eavesdropper) undergo the $\alpha -\mu $ fading statistics and the FSO link experiences the exponentiated Weibull fading statistics. Exploiting the amplify-and-forward (AF) relaying scheme while considering two detection techniques (i.e. heterodyne detection and intensity modulation/direct detection) with pointing error impairments, the mathematical formulations of the unified probability density function and cumulative distribution function are performed for the equivalent signal-to-noise ratio of the considered dual-hop RF-FSO link. Closed-form analytical expressions for average secrecy capacity, secrecy outage probability, and the probability of non-zero secrecy capacity are derived in terms of Meijer's $G$ and Fox's $H$ functions to quantify the system performance. Capitalizing on these expressions, the secrecy performance is further analyzed for various channel parameters of RF links, aperture sizes of the receiver, pointing errors, and atmospheric turbulence severity. The results reveal that aperture averaging can improve the secrecy performance remarkably by suppressing the effects of turbulence. Monte Carlo simulations are provided to justify the accuracy of the proposed model.